 Dear student, this is the another example of the multivariate multiple regression. In this example, we have two dependent variables and the two independent variables. So how will we handle that in multivariate multiple regression? How will we estimate its value? Now here is the example. Estimate the best linear regression model of this. This is the dependent variable from the following data. Now we have the data. These are the two dependent variable and these are the two independent variable. Y1, Y2 and the X1, X2. Now we have to determine the linear regression model with two independent variables. And I will solve this example in R. We will check it in R. So in R, this is the window of R. Now the Y1 is the dependent variable which is equals to Y1, C, parenthesis, data interconnection. Y1 is the 1, 3, 5, 7 and 9. Y2 equals to C. Y2 is the dependent variable 1, 1, 2, 3, 3. So X1 is the independent variable C. 0, 2, 3, 3, 4. X2 is the independent variable C. 1, 1, 1, 2, 2. Now Y1, Y2, X1, X2. We have all the values. Now I have to fit multivariate multiple regression on this. These are the two dependent variables and these are the two independent variables. So this is the notation M1, L1, multivariate multiple regression equals to Lm, linear regression, parenthesis, C-bind. Combine which is Y1, Y2. These are the dependent variables, 10s to X1 plus X2. These are the independent variables. So I have to do multiple regression model. Highlight, then run. This is Y1, X1. So this is the model. Y1, Y2 equals to regression model. So minus 1.7742 plus 1.3548X1 plus 2.5161X2. So this is the model for Y1. Then you have the model for Y2. This is the beta 0, beta 1, beta 2 minus 0.2903 plus 0.2581X1 plus 1.1935X2. So what do you have? Simultaneously, two dependent and two independent we have run. So you have the model for Y1 generated and for Y2 generated. Further, if you want to see its summary, then we have a command. Summary, we have to check the summary. Whose? M1L1. This is not a part of the question. We are just checking its summary. We have also seen the summary. What happened to you? I will check it for you. Simultaneously, we have run it. Now look at this. This is the response for Y1. If we do it individually, it comes for LMY1. We have the results. Now the coefficients are the same. This is the result of estimated values. This is beta 0, beta 1, beta 2. Then we will see the response for Y2. So you have the same result. This is the beta 0, beta 1 and beta 2. We have also checked the summary. We have also checked the individual. The summary will give you P value, T standard error. We had to see the estimated values. We have also checked the estimated values. We have the results of model fitting. We have seen the results of the summary. The summary is better. It will interpret you better. Because you have the result of the standard error, T result and its significance, P, according to the idea. This is the example of the multivariate multiple regression and we have the two dependent and the two independent variables. Two independent, two independent variables when we run them simultaneously, the same results are there if we solve it according to the univariate. The same results are there. But what did multivariate do? It reduced the time. The result will not make any difference with our multivariate and univariate. But time is reduced. Simultaneously, these are used in multivariate multiple regression results.